Mixed finite elements for Bingham flow in a pipe
Tom Gustafsson, Philip L. Lederer
TL;DR
This paper develops a new finite element method for modeling Bingham fluid flow in pipes, providing stability analysis and adaptive refinement techniques supported by numerical experiments.
Contribution
Introduces a novel a priori and a posteriori error analysis for mixed finite element approximations of Bingham flow, enabling stable and adaptive solutions.
Findings
Proves stability for various conforming finite elements.
Demonstrates effectiveness of adaptive mesh refinement.
Validates theory with numerical examples.
Abstract
We consider mixed finite element approximations of viscous, plastic Bingham flow in a cylindrical pipe. A novel a priori and a posteriori error analysis is introduced which is based on a discrete mesh dependent norm for the normalized Lagrange multiplier. This allows proving stability for various conforming finite elements. Numerical examples are presented to support the theory and to demonstrate adaptive mesh refinement.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Lattice Boltzmann Simulation Studies · Fluid Dynamics and Turbulent Flows